The market for home networking is developing at a phenomenal rate. Service providers from cable television, telephony and digital subscriber line markets are vying to deliver bundled services such as basic telephone service, Internet access and entertainment directly to the consumer. Collectively these services require a high-bandwidth network that can deliver 30 Mbits/s or even high rates. The Institute of Electrical and Electronic Engineers (IEEE) 802.11a standard describes a cost-effective, robust, high-performance local-area network (LAN) technology for distributing this multimedia information within the home. Networks that will operate in accordance with standard 802.11a will use the 5-GHz UNII (unlicensed National Information Infrastructure) band and may achieve data rates as high as 54 Mbits/s, a significant improvement over other standards-based wireless technology. The 802.11a standard has some unique and distinct advantages over other wireless standards in that it uses orthogonal frequency-division multiplexing (OFDM) as opposed to spread spectrum, and it operates in the clean band of frequencies at 5 GHz.
OFDM is a technology that resolves many of the problems associated with the indoor wireless environment. Indoor environments such as homes and offices are difficult because the radio system has to deal with a phenomenon called “multipath.” Multipath is the effect of multiple received radio signals coming from reflections off walls, ceilings, floors, furniture, people and other objects. In addition, the radio has to deal with another frequency phenomenon called “fading,” where blockage of the signal occurs due to objects or the position of a communications device (e.g., telephone, TV) relative to the transceiver that gives the device access to the cables or wires of the cable TV, telephone or internet provider.
OFDM has been designed to deal with these phenomena and at the same time utilize spectrum more efficiently than spread spectrum to significantly increase performance. Ratified in 1999, the IEEE 802.11a standard significantly increases the performance (54 Mbits/s vs. 11 Mbits/s) of indoor wireless networks.
The ability of OFDM to deal with multipath and fading is due to the nature of OFDM modulation. OFDM modulation is essentially the simultaneous transmission of a large number of narrow band carriers sometimes called subcarriers, each modulated with a low data rate, but the sum total yielding a very high data rate. FIG. 1a illustrates the frequency spectrum of multiple modulated subcarriers in an OFDM system. To obtain high spectral efficiency the frequency response of the subcarriers are overlapping and orthogonal, hence the name OFDM. Each narrowband subcarrier can be modulated using various modulation formats such as binary phase shift keying (BPSK), quatenary phase shift keying (QPSK) and quadrature amplitude modulation QAM (or the differential equivalents).
Since the modulation rate on each subcarrier is very low, each subcarrier experiences flat fading in multipath environment and is easy to equalize, where coherent modulation is used. The spectrums of the modulated subcarriers are not separated but overlap. The reason why the information transmitted over the carriers can still be separated is the so called orthogonality relation giving the method its name. The orthogonality relation of the subcarriers requires the subcarriers to be spaced in such a way that at the frequency where the received signal is evaluated all other signals are zero. In order for this orthogonality to be preserved it helps for the following to be true:                1. Synchronization of the receiver and transmitter. This means they should assume the same modulation frequency and the same time-scale for transmission (which usually is not the case).        2. The analog components, part of transmitter and receiver, are of high quality.        3. The multipath channel needs to accounted for by placing guard intervals which do not carry information between data symbols. This means that some parts of the signal cannot be used to transmit information.        
Due to bandwidth limitations and multipath propagation, the transmission channel between the transmitter and receiver distorts the signal being transmitted, leading to inter symbol interference (ISI). The receiver needs to identify this channel distortion (or channel estimate) and account for its effect by using the channel estimate to equalize data. One method for determining the channel estimate involves transmission of a training sequence, i.e. a set of fixed data that are known to both transmitter and receiver. By examining how the known, fixed data is modified by the channel, actual random data can be adjusted, improving information throughput.
A channel estimate can be made by transforming time domain samples of the training sequence into the frequency domain to determine the frequency spectrum of the training sequence as received at the receiver. Since the training sequence is known, the frequency spectrum of the training sequence as transmitted from the transmitter can be derived. The quotient of the frequency spectrum of the training sequence as received at the receiver and the frequency spectrum of the training sequence as transmitted from the transmitter is the channel estimate or transfer function of the channel. Before the channel estimate is used to adjust the frequency domain representation of received data, it can be smoothed and inverted which involve additional mathematical operations. Mathematical operations with numbers that have finite precision almost invariably result in information being lost due to rounding and other errors. This loss of information is often not very consequential. However, if the values in the sequence of samples of the channel estimate are relatively small and the precision of the format in which the values are stored is relatively low, the operations of smoothing and inversion may result in relatively significant information about the channel estimate being lost. The loss of information can be significant enough to impair successful recovery of random data, decreasing throughput.
Possible solutions for preventing too much loss of information include representing values in floating point format, and having a large number of bits to accommodate both small and large signals. Floating point representation typically suffers from relatively high power consumption and relatively slow execution speed. Using a large number of bits consumes relatively large amounts of hardware and power and may not satisfy the need for both large dynamic range and high precision. The size of the fraction that can be represented by the smallest bit in the number format is the precision of the format. The size of the largest number that can be represented is the dynamic range of the number.
As described above, existing solutions are not capable of providing a representation of the channel estimate that does not consume relatively large amounts of hardware and power and is able to stem significant loss of information when operations are performed on the representation. Consequently, it is desirable to provide a solution that overcomes the shortcomings of existing solutions.